few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
E. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
F. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


Thought: In this problem, students learn to recognize equivalent fractions. That is, three laps around the playground is 3/12 mile, which is equivalent to 1/4, which is one lap around the school.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000212

4
options: Investigate chance processes and develop, use, and evaluate probability models.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Investigate patterns of association in bivariate data.

Draw informal comparative inferences about two populations.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Develop understanding of statistical variability.

Understand independence and conditional probability and use them to interpret data.

Interpret linear models.

Calculate expected values and use them to solve problems.

Use random sampling to draw inferences about a population.

Use probability to evaluate outcomes of decisions.

Summarize and describe distributions.

Understand and evaluate random processes underlying statistical experiments.

Summarize, represent, and interpret data on a single count or measurement variable.
problem_activity: Activity
In this activity, students are asked to interpret in context the slope and vertical intercept of a linear model given a scatter plot and the equation for a linear model that fits the data well. The linear model is also used to interpolate and extrapolate information about the data in context.
Monitor for students who:
estimate values based on the graph
use the equation for the linear model to find the values
Launch
Arrange students in groups of 2.
Student Facing
The scatter plot shows the sale price of several food items,
\(y\)
, and the cost of the ingredients used to produce those items,
\(x\)
, as well as a line that models the data. The line is also represented by the equation
\(y = 3.48x + 0.76\)
.
[IMG]
What is the predicted sale price of an item that has ingredients that cost \$1.50? Explain or show your reasoning.
What is the predicted ingredient cost of an item that has a sale price of \$7? Explain or show your reasoning.
What is the slope of the linear model? What does that mean in this situation?
What is the
\(y\)
-intercept of the linear model? What does this mean in this situation? Does this make sense?
Student Response
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for free access to Student Response.
Anticipated Misconceptions
Although the grid in the picture does not look like squares, each line in both the horizontal and vertical directions are 0.5 apart. Tell students who are confused to look at the values listed on the axes and identify the values attached to a few of the grid lines.
Activity Synthesis
The purpose of this discussion is for students to describe where to find the slope and vertical intercept from a scatter plot and interpret the values in terms of the context.
Select previously identified students to share in the order listed in the narrative. Ask students:
“Are the values obtained from looking at the graph close to the values calculated using the equation?” (Yes, the values are close.)
“Which method will you use to predict values based on the model?” (Maybe a mixture of both methods. Using the equation produces a more precise value from the model, but it is also important to look at the graph to get a sense of how well the model fits the data where I am predicting.)
“Why do you think the intercept for the model is not
\((0,0)\)
?” (Companies may still try to charge money for items that cost nothing to produce. They need to pay for the salaries of their workers, research and development, as well as other things that require the company to make money more than just the cost of making the item. It may also be the case that it does not make sense to interpret the
\(y\)
-intercept, since we have no evidence to believe that the same linear relationship will hold there.)
Reading, Writing, Speaking: MLR3 Clarify, Critique, Correct.
Before students share their interpretations of the slope, present an ambiguous explanation. For example: “The slope means that as sales increase, the cost of ingredients increases.” Ask students to identify inaccuracies, critique the reasoning, and write a correct explanation. As students discuss with a partner, listen for students who identify and clarify the ambiguous language in the statement. Invite students to share their critiques and corrected explanations with the class. Listen for and amplify the language students use to describe what happens to the sale price when the cost of ingredients increases by
$
1. This helps students evaluate, and improve on, the written mathematical arguments of others, as they clarify the meaning of slope in context.
Design Principle(s): Optimize output (for explanation); Maximize meta-awareness
Action and Expression: Internalize Executive Functions.
Provide students with a two-column graphic organizer. Label one column “graph” and another column “equation.” Ask students to transfer their answers into the corresponding column on their organizer. When the whole group shares, they can continue to use the organizer capturing the answer if anyone used the alternative method for each question.
Supports accessibility for: Language; Organization


correct_option_index: 8